1. Field of the Invention
This invention relates generally to methods for displaying the results of prescribed tests (e.g., medical tests administered to patients) and, more particularly, to methods that provide two-dimensional displays of such test results.
2. Description of the Related Art
In the field of medicine, diagnostic tests, prognostic tests, and functional evaluations are administered to patients to provide information that can be used by the physician to ascertain the patient's medical condition. It is recognized, however, that the results of such tests and evaluations should not be considered in isolation, but rather should be considered along with other factors pertinent to the evaluation, e.g., a pretest, or a priori, probability of a disease or condition being present. Such other factors that should be considered might include, for example, the results of earlier tests on the same patient, the patient's family history, gender, age, and so on. By taking such factors into account when evaluating the results of a test of this kind, a more accurate evaluation of the patient's condition can be made.
The need to consider pretest probabilities derives from the unfortunate fact that most medical tests are not 100% reliable in indicating whether or not a medical condition is present, or if present the extent of that condition. In almost all cases, a certain percentage of tests administered to patients actually having a disease will indicate that the disease is not present (i.e., false negatives), while a certain unrelated percentage of tests administered to patients not having the disease will result in positive test results (i.e., false positives). By making proper use of evidence indicative of pretest probabilities, the effect of those uncertainties in the significance of the test results can be minimized.
Presented below are three examples of test analyses incorporating the consideration of pretest probabilities. In the first example, the patient has a high pretest probability of having a particular disease, in the second example a low pretest probability, and in the third example an intermediate pretest probability. In all three examples, the probability of a diseased patient testing positive, i.e., the test's sensitivity, is 0.7, while the probability of a non-diseased patient testing negative, i.e., the test's specificity, is 0.9.
In the first example, a patient is selected from a group of 5000, 4500 of whom have coronary-artery disease, with at least 50% diameter narrowing of one or more major vessels. The pretest probability of disease is therefore 90%, which happens to correspond roughly to that for middle-aged men having typical angina pectoris. Because of the test's sensitivity of 0.7 and specificity of 0.9, it follows that testing all 5000 patients would lead to 0.7.times.4500, or 3150, true-positive test results and (1-0.9).times.500, or 50, false-positive test results. Thus, 3150 of the combined 3200 positive test results would in fact be correct. This corresponds to a post-test, or posterior, likelihood of 98.4% that a positive test represents a confirmation that a particular patient is in fact diseased.
Conversely, in the case of a negative test result in this same population of 5000 patients, 4500 of whom are diseased, (1-0.7).times.4500, or 1350, false-negative test results will be observed among the diseased patients, and 0.9.times.500, or 450, true-negative test results will be observed among the non-diseased patients. Thus, 1800 negative test results would be observed, 1350 of them being false negatives and 450 true negatives. The post-test probability of disease in a patient for whom a negative test result is obtained therefore is 75%. In other words, for a particular patient selected from this population, a negative test result indicates that that patient still has 75% probability of being diseased.
Summarizing the results of the first example, which covers a population of patients for whom the pretest probability of disease is 90%, a positive test result increases the probability of disease from 0.9 to 0.984, while a negative test result reduces the probability of disease from 0.9 to 0.75.
In the second example, the same test is administered to a population of 5000 patients, this time only 250 of whom are diseased. This corresponds to a pretest disease probability of only 5%, which is similar to that of an asymptomatic population. In this example, true-positive test results will be produced for 0.7.times.250, or 175, while false-positive test results will be produced for (1-0.9).times.4750, or 475. The post-test probability of disease for any individual for whom a positive test is produced therefore is 175/(175+475), or 26 9%. A positive test result therefore is not particularly meaningful, since false positives outnumber true positives by a ratio of almost 3 to 1.
In the case of a negative test result, (1-0.7).times.250, or 75, false-negative tests will be observed in the diseased patients, while 0.9.times.4750, or 4275, true-negative test results will be observed in the non-diseased patients. Thus, the post-test probability of disease in the negative test population is 75/(75+4275), or merely 1.7%.
Thus, for patients having a pretest disease probability of only 5%, a positive test result increases the probability from 5% to 26.9%, while a negative test result reduces the probability from 5% to 1.7%.
Finally, in the third example, the same diagnostic test is administered to a population of 5000, this time 50% of whom are diseased. True positive results will therefore number 0.7.times.2500, or 1750, while false positive results will number (1-0.9).times.2500, or 250. The post-test probability of disease for a patient receiving a positive test result therefore will be 1750/(1750+250), or a 87.5%. Conversely, false-negative test responses among diseased patients will number (1-0.7).times.2500, or 750, while true-negative responses among nondiseased patients will number 0.9.times.2500, or 2250. The post-test probability of disease for a patient with a negative test therefore will be 750/(750+2250), or 25%. The diagnostic test is therefore particularly meaningful for patients in this population, for whom the disease prevalence is 50%. Positive test results will increase the probability of disease from 50% to 87.5%, while negative test results will reduce the probability of disease from 50% to 25%.
Although the analysis described above is known in the art, it is not readily appreciated or followed by all physicians who are called upon to analyze the results of diagnostic, prognostic and functional tests and offer informed medical judgments. For one reason or another, the analysis is not properly followed. There is therefore a need for a method that makes the necessary adjustments to the results of medical tests to incorporate pretest or a priori probabilities, and to display the adjusted information in a manner that is more likely to be accepted by the evaluating physician. The present invention fulfills this need.